Question

What is the approximate diameter of a sphere with a volume of 523 cm^3

Answer 1

Step 1

Write perimeters out

Volume = 523cm^3

`\pi\text{ = }(22)/(7)`

Radius , r = ?

Diameter = 2r

Step 2

Next write out formula of volume of sphere

`\text{Volume of sphere = }(4)/(3)\text{ }\pi r^3`

Step 3

Next substitute your values

`\begin{gathered} ^{}^{} \\ \text{Volume of a sphere = }(4)/(3)\text{ }\pi r^3 \\ 523\text{ = }(4)/(3)\text{ }*\text{ }(22)/(7)xr^3 \\ 523\text{ = }(88r^3)/(21) \\ \text{next cross multiply} \\ 88r^3\text{ = 523 x 21} \\ 88r^3\text{ = 10983} \\ \text{Divide through by 88} \\ r^3\text{ = }(10983)/(88) \\ r^3\text{ = 124.8} \\ r\text{ = }\sqrt[3]{124.8} \\ r\text{ = 4.99cm} \end{gathered}`

Diameter = 2 x r

= 2 x 4.99

= 9.98

= 10cm